This invention concerns improvements to gravity gradient instruments (GGI), and in particular to the accelerometers that are paired within these instruments.
The GGI consists of two pairs of high quality, low noise, matched accelerometers mounted on a block. Each of the accelerometers has an internal feedback loop for proper operation, and an external feedback loop for trim adjustment of the accelerometer scale factor and alignment of the accelerometer sensitive axis.
The normal configuration has the accelerometers mounted in opposing pairs, and equally spaced around the circumference of a circle, with their sensitive axes tangential to the circle. In use the block is rotated about a spin axis which is perpendicular to the plane of the circle, and passes through the centre of the circle. The outputs of the accelerometers of each pair are differenced and the difference signals are then combined. The overall effect is that the large common mode accelerometer output signals cancel to a high degree of precision, so that the residual differences which constitute the gradient signal are observable.
The accelerometers must be matched in their pairs so that the current/acceleration transfer function is matched in amplitude and phase at all frequencies of interest, to an accuracy of 1 part in 1010. The mismatch in accelerometer pairs is a result of the difference of the internal feedback closed loop errors, and thus the mismatch is also inversely proportional to the open loop gain. The existing external feedback scale factor adjustment can degrade, by an order of magnitude, the high frequency ( greater than 1 Hz) lateral sensitivity for a 2% mismatch within the accelerometers. The influence of vertical acceleration on the accelerometers is an additional complicating factor.
The invention, as currently envisaged, is all accelerometer having a proof mass suspended by a spring within a magnetic field. An internal feedback loop provides a signal related to movement of the proof mass back through a reaction coil retaining the proof mass in the magnetic field, to maintain the proof mass stationary. An external feedback loop adjusts the accelerometer scale factor. Wherein, the internal feedback loop provides second order compensation to the proof mass and the spring stiffness.
The internal feedback path may include high gain to reduce errors in the accelerometer transfer function.
A compensator in the internal feedback loop may provide double pole and double zero compensation:                     m        1            ⁢              s        2              +          k      1                          m        0            ⁢              s        2              +          k      0      
where:
m1 is the mass of the proof mass
k1 is the spring constant of the spring
m0 is a nominal proof mass and
k0 is a nominal spring constant.
The nominal proof mass and spring constant represent the accelerometer characteristics to which both accelerometers of a pair are to be matched in order that the two accelerometers are closely matched to each other.
In a GGI the compensation provided by the internal feedback loop may correct for the mass ratio (or Fo frequency ratio) mismatch between two paired accelerometers by providing the s2 loop gain term as a mass compensator. The compensation may also correct for the spring ratio by providing a loop gain term which lumps together variations in pick-off gain, integrator capacitors and spring constant, as a spring stiffness k compensator.
The components of the compensation network are typically resistors and capacitors. Variable components are introduced so that the break frequencies can be tuned over a +/xe2x88x925% range to match the masses m and the spring stiffnesses k of the accelerometer pairs to better than 0.5%. The closed loop gain blocks are trimmed in pairs to match the time constants to within 0.5%.
In a further aspect the invention is a method of matching accelerometer pairs, comprising the steps of:
Testing the pair of accelerometers in back to back fixtures on a horizontal shaker which is aligned to the same vertical angle as in the GGI.
Selecting the accelerometers on the basis of the best scale factor match at 0.5 Hz and the lowest lateral sensitivity at 10 Hz.
Applying horizontal excitation at 0.25 Hz, 1 Hz and 10 Hz (or higher) and detecting the system response with synchronous demodulation at the frequencies. A scale factor loop may be driven from the 0.25 Hz signal or it may be adjusted manually while the excitation is applied.
Adjusting second order mass compensation to minimise the in phase (I) and the quadrature (Q) components of the signal at 10 Hz.
Adjusting second order spring stiffness compensation to minimise the components at 1 Hz.
Iteratively repeating the adjusting steps to achieve matches better than 0.5%.
The external feedback path may provide the output signal, demodulated at the spin frequency xcexa9 by a demodulator, to correct for mismatches in the strength B of the magnets in accelerometers. This feedback loop may also compensate for some part of the mismatches in proof mass and spring stiffness.